US-EGMO-TST 2023 Problem 4

Let $ABC$ be a triangle with $AB+AC=3BC$ . The $B$ -excircle touches side $AC$ and line $BC$ at $E$ and $D$ , respectively. The $C$ -excircle touches side $AB$ at $F$ . Let lines $CF$ and $DE$ meet at $P$ . Prove that $\angle PBC = 90^{\circ}$ .

Ray Li